#### lie.tst1.7 KB Permalink History Raw

 1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677787980818283848586878889909192 ``````% test file for the Lie package % 1. n-dimensional Lie algebras with dimL1=1 % n=6 array lienstrucin(6,6,6)\$ lienstrucin(1,2,2):=lienstrucin(1,2,6):=lienstrucin(1,5,2):=-1\$ lienstrucin(1,5,6):=lienstrucin(2,5,3):=lienstrucin(2,5,5):=-1\$ lienstrucin(1,2,3):=lienstrucin(1,2,5):=lienstrucin(1,5,3):=1\$ lienstrucin(1,5,5):=lienstrucin(2,5,2):=lienstrucin(2,5,6):=1\$ liendimcom1(6); % transformation matrix lientrans; clear lienstrucin\$ % n=8 array lienstrucin(8,8,8)\$ lienstrucin(1,2,2):=lienstrucin(1,5,2):=lienstrucin(2,4,3):=1\$ lienstrucin(2,4,5):=lienstrucin(4,5,2):=1\$ lienstrucin(1,2,3):=lienstrucin(1,2,5):=lienstrucin(1,5,3):=-1\$ lienstrucin(1,5,5):=lienstrucin(2,4,2):=lienstrucin(4,5,3):=-1\$ lienstrucin(4,5,5):=-1\$ lienstrucin(1,2,6):=lienstrucin(1,5,6):=lienstrucin(4,5,6):=5\$ lienstrucin(2,4,6):=-5\$ liendimcom1(8); % same with verbose output on tr_lie\$ liendimcom1(8); clear lienstrucin\$ off tr_lie\$ % 2. 4-dimensional Lie algebras % Korteweg-de Vries Equation: u_t+u_{xxx}+uu_x=0 % symmetry algebra spanned by four vector fields: % v_1=d_x, v_2=d_t, v_3=td_x+d_u, v_4=xd_x+3td_t-2ud_u array liestrin(4,4,4)\$ liestrin(1,4,1):=liestrin(2,3,1):=1\$ liestrin(2,4,2):=3\$ liestrin(3,4,3):=-2\$ lieclass(4); clear liestrin\$ % dimL1=3, dimL2=3 array liestrin(4,4,4)\$ liestrin(1,2,1):=-6\$liestrin(1,2,3):=-2\$liestrin(1,2,4):=6\$ liestrin(1,3,1):=-1\$liestrin(1,3,2):=1\$liestrin(1,3,4):=1\$ liestrin(2,3,1):=-3\$liestrin(2,3,4):=2\$ liestrin(2,4,1):=6\$liestrin(2,4,3):=2\$liestrin(2,4,4):=-6\$ liestrin(3,4,1):=1\$liestrin(3,4,2):=-1\$liestrin(3,4,4):=-1\$ lieclass(4); % same with verbose output on tr_lie\$ lieclass(4); % transformation matrix liemat; clear liestrin\$ off tr_lie\$ end\$ ``````